Method of determining shear stress employing a monomer-polymer laminate structure

ABSTRACT

The laminate structure comprises a liquid crystal polymer substrate attached to a test surface of an article. A light absorbing coating is applied to the substrate and is thin enough to permit bonding steric interaction between the liquid crystal polymer substrate and an overlying liquid crystal monomer thin film. Light is directed through and reflected by the liquid crystal monomer thin film and unreflected light is absorbed by the underlying coating. The wavelength of the reflected light is indicative of the shear stress experienced by the test surface.

ORIGIN OF THE INVENTION

The invention described herein was made jointly by an employee of theUnited States Government and contract employees under NASA Contracts. Inaccordance with 35 U.S.C. 202, the contractors elected not to retaintitle.

This is a divisional of copending application Ser. No. 07/849,612 filedon Mar. 2, 1992, now U.S. Pat. No. 5,223,310.

BACKGROUND OF THE INVENTION

1. Technical Field of the Invention

The present invention relates generally to shear stress determinationand more particularly to determining shear stress via changes in lightwavelengths reflected via a monomer-polymer liquid crystal system.

2. Discussion of the Related Art

Cholesteric liquid crystals, monomers as well as polymers, demonstratethe phenomenon of selective reflection where incident white light isreflected in such a way that its wavelength is governed by theinstantaneous pitch of the helix structure of these phases. The helicalstructure can be modulated by thermodynamic as well as mechanicalperturbations, e.g., by changing the temperature or by applying anexternal stress field. The helix pitch may, however, be compensated fortemperature effects, thereby leaving it sensitive only to external shearstress. Because of the high viscosity of liquid crystal polymers (LCPs),the shear stress fields required for helix structure modulation incholesteric LCPs are very high and therefore LCPs are not goodcandidates for low shear indicators. Shear sensitive, but temperatureinsensitive, monomer cholesteric liquid crystals are low viscosityphases and their structure can be modulated by relatively low stressfields. As a result, monomer cholesteric liquid crystals have foundapplication in flow visualization and surface temperature measurement inaerodynamic testing as well as in subsonic and supersonic wind tunnelexperiments. Many of these experiments have provided significantqualitative information about the flow field. These experiments have notbeen so successful in providing quantitative data on the flowparameters, especially when the liquid crystal thin films on modelsurfaces are exposed directly to the wind flow. The lower viscosity ofthe monomer liquid crystals combined with the poor wettability of theconventional model surfaces results in the thinning and ultimatelywashing out of the liquid crystal when exposed to wind flow. As aconsequence, the selective reflection characteristics of the modelsurface on which a monomer cholesteric thin film has been applied becometime dependent for a given rate of wind flow.

OBJECTS OF THE INVENTION

It is accordingly an object of the present invention to measure shearforces on an article.

It is another object of the present invention to measure shear forces onan article quantitatively.

It is a further object of the present invention to measure shearstresses on an article surface exposed directly to an air flow.

It is yet another object of the present invention to measure shearforces on an article while maintaining sufficient wettability for ashear sensitive monomer liquid crystal overlying the article.

Other objects and advantages of the present invention are apparent fromthe drawings and specification of the present invention.

SUMMARY OF THE INVENTION

The foregoing and additional objects are obtained by a shear sensitivelaminate structure and method of using the same according to the presentinvention. The laminate structure comprises a liquid crystal polymersubstrate attached to a test surface of an article. A light absorbingcoating is applied to the substrate and is thin enough to permit bondingsteric interaction between the liquid crystal polymer substrate and anoverlying liquid crystal monomer thin film. Light is directed throughand reflected by the liquid crystal monomer thin film whereasunreflected light is absorbed by the underlying coating. The wavelengthof the reflected light is indicative of the shear stress experienced bythe test surface.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view of the monomer-polymer liquid crystal laminateaccording to the present invention;

FIG. 2 is a drawing of a surface texture micrograph of an injectionmolded liquid crystal polymer substrate used in the present inventionviewed in reflection with polarizers crossed and an objectivemagnification of 4×;

FIG. 3(a) is a drawing of the micrograph of a monomer liquid crystalthin film mounted directly on a liquid crystal polymer substrate of FIG.2 viewed under the preceding conditions except that the objectivemagnification is 40×;

FIG. 3(b) is a drawing of the micrograph of FIG. 3(a) wherein the colorchanges from red to yellow due to air impingement in the direction ofthe arrow having a force of approximately 65 mmHg;

FIG. 3(c) is a drawing of a free surface texture micrograph of a monomerliquid crystal thin film mounted on a blackened metal surface with noforce, viewed in reflection with the polarizers crossed and an objectivemagnification of 40×;

FIG. 3(d) is a drawing of the micrograph of FIG. 3(c) wherein acontinuous air flow in the direction of the arrow and having a force ofapproximately 65 mmHg washes the monomer out of the monomer liquidcrystal surface;

FIG. 4 is a schematic of an experimental setup according to the presentinvention;

FIG. 5(a) graphs the variation of reflected light intensity of amonomer-polymer liquid crystal laminate according to the presentinvention as a function of gas flow differential pressure wherein λ=580nm;

FIG. 5(b) is a graph similar to FIG. 5(a) except that λ=600 nm;

FIG. 6 is a graph of the linear relationship between the reflectedwavelength and differential pressure;

FIG. 7(a) is a geometrical representation of the helical structure ofthe free surface of the monomer liquid crystal with no force in theX-direction;

FIG. 7(b) is a representation of light waves reflected by the structureof FIG. 7(a);

FIG. 7(c) is similar to FIG. 7(a) except that a force is exerted in theX-direction; and

FIG. 7(d) is a representation of light waves reflected by the structureof FIG. 7(c).

DETAILED DESCRIPTION OF THE INVENTION

The molecular chirality and an associated macroscopic twist are the twobasic characteristics of a cholesteric liquid crystal order. Togetherthey produce a helix structure whose pitch p is typically a fewwavelengths of visible light. Selective reflection is a unique featureof the helix structure and occurs when the optical pathlength (np)equals the wavelength (λ) of the incident light, i.e., λ=np, where n isthe average refractive index of the liquid crystal. Birefringence(Δn=n_(e) -n_(o) ˜0.2), a characteristic property of a system of longlinear molecules, does not allow the wavelength (λ_(s)) of the selectivereflection to be sharp. Consequently for an incident while light areflected light bandwidth Δλ=p(n_(e) -n_(o))=(Δn/n)λ, where n_(e) andn_(o) are the refractive indices parallel and perpendicular,respectively, to the molecular director in the same plane, is observed.For a shear sensitive cholesteric liquid crystal, it is known that thepitch of the helical texture normally follows an inverse shear stressdependence as is evident from recent selective reflection measurements.When the shear stress is increased the gradual winding of the helix isvisualized in reflection as a dramatic color change from red to blue foran incident white light.

The present invention utilizes the selective reflection properties of ashear sensitive monomer liquid crystal thin film overlying an uppersurface of a liquid crystal polymer substrate. Wavelength λ_(s) for theselected reflection from the system is determined by measuring theintensity of the reflected light from the liquid crystal free surface asa function of the air flow differential pressure ΔP.

Referring to FIG. 1, a monomer-polymer liquid crystal (MPLC) laminatestructure 10 is seen to comprise flat substrate 12 of liquid crystalpolymer (LCP) formed on a test surface of an article T. The uppersurface of the LCP substrate 12 is coated with a light absorbing blackcoating 14. A monomer cholesteric liquid crystal (MLC) thin film 16overlies the coating 14. This laminate structure 10 is discussed ingreater detail below.

A LCP flat substrate 12 was made by the process of injection molding.The embodiment tested and discussed below used XYDAR® SRT-800 brand LCPhigh strength resin, which is a wholly aromatic liquid crystalproprietary polyester made by Amoco Performance Products, Inc. andtrademarked and distributed by Dart Industries, Inc. The XYDAR® SRT-800brand LCP can be formed into a plastic having a strength approachingsteel but a weight as light as aluminum and having a high meltingpoint >350° C. Such a high performance LCP has shown stronger liquidcrystallinity of the polymer chain orientation on the surface than inthe bulk formed during the process of molding. The LCP substrate isaffixed to a test surface of article T by any suitable means such asclamps, adherands, tape, etc.

VECTRA® A130 LCP high strength resin, which is a wholly aromatic liquidcrystal polyester distributed by Vectra, Inc., was also investigated asa possible candidate for the substrate but was not selected because ofits inadequate wettability with the overlying monomer layer.

As the LCP is molded from the resins in the form of globules, surfaceorientation of the polymer chains becomes visible in the form of aplanar aligned texture. The LCP being opaque, its free surface texturewas examined in reflection under crossed polarizers on an opticalpolarizing microscope such as Optihot-Pol brand microscope, availablefrom Nikon. A particularly preferred optical arrangement is described inD. S. Parmar, Rev. Sci. Instruments, 62, 474 (1991). The micrograph ofthe surface texture of an LCP surface under crossed polarizers is shownin FIG. 2 where the direction of the polarizer is along the horizontalstriations. The black color of the texture clearly demonstrates theliquid crystalline order of molecular orientation on the surface. Theremarkable feature of the texture is the presence of the alignmentdefects in the shape of parabolas. Furthermore, a series of faint crosslines indicate a strong cross-linkage of the polymer main chains and theside chains even on the surface of this material.

The LCP substrate upper surface was coated with flat, black lacquerspray paint in order to absorb the unreflected light. The black coating14 is thick enough to absorb light which is unreflected by the monomerliquid crystal film 16, but also thin enough to maintain strong stericinteractions between the LCP and the overlying monomer cholestericliquid crystal thin film 16 (˜20 μm) applied over the black coating. Theabsorbing coating increases the contrast of the reflected light andreduces the signal to noise ratio. The particular black paint used inthe described embodiment is BB-G1, marketed by Hallcrest, Inc.

The polymer chain orientations on the upper surface of LCP substrate 12are expected to induce adequate wettability as well as formation of astable Grandjean texture in the overlying monomer liquid crystal thinfilm 16 due to surface steric interactions. The particular monomer is ashear sensitive cholesteric liquid crystal TI 511 available from E.M.Industries of New York.

The monomer-polymer liquid crystal (MPLC) laminate structure 10 thusobtained was investigated by reflection polarization microscopy. TheMPLC laminate free surface texture, shown in the micrographrepresentation of FIG. 3(a), clearly demonstrates a strong planarorientation, i.e., a Grandjean texture, of the monomer liquid crystal.Since no other surface treatment has been used for the monomer alignmenton the LCP substrate, the planar orientation of the monomer is inducedpurely by the liquid crystalline order on the monomer-polymer interface.

The free surface of the monomer liquid crystal is exposed to air fieldfrom a small jet in the plane of the monomer-polymer interface along thedirection of the polymer chains on the LCP surface, as discussed belowin reference to FIG. 4. The black crosses on the monomer liquid crystal(MLC) surface in FIG. 3(a) disappear as the air jet flows on the surfacein the direction of the arrow shown in FIG. 3(b). The shear stress (F˜65mmHg) due to the air impingement changes the reflection color fromcopper red toward yellow. The MLC texture applied directly on a metalsurface per conventional methods in the absence and in the presence of ashear stress F is shown in the micrographs of FIGS. 3(c) and 3(d)respectively. Two distinct features of the texture in FIGS. 3(c,d) incomparison to FIGS. 3(a,b) are: (i) for F=0, the Grandjean texture ofFIG. 3(c) on a metal surface is not as good as that of FIG. 3(a) for theLCP surface; and (ii) the liquid crystal is washed out of the substratesurface due to continuous flow of air as evident from the appearance ofthe black coating on the metal surface in FIG. 3(d). As a result of thismaterial flow, the reflected light intensity becomes time dependentcreating lack of definite information on flow visualization. It shouldalso be noted here that, because of the lack of steric interactions onthe metal surface, the texture of MLC changes from Grandjean to focalconic soon after the shear stress is removed, thereby making the resultsirreversible.

The shear sensitivity of the MPLC system according to the presentinvention was measured with the experimental system whose schematicdiagram is given in FIG. 4. The MPLC laminate 10 comprised of the XYDAR®SRT-800 brand LCP substrate 12 (˜5 cm×5 cm), a thin black coating 14 asdescribed and the monomer liquid crystal thin film 16 TI 511 (˜20 μm),is mounted in the horizontal plane on a rigid platform RP. An air jet isdirected through a standard system comprising a control valve 20, a flowmeter 22 and a pressure gauge 24 and is allowed to impinge parallel tothe plane of the MLC thin film 16. Light from a microprocessorcontrolled monochromator 26, such as a Digikron 240 commerciallyavailable from CVI Laser Corporation and having a spectral resolution of0.6 Å, is passed through an appropriate optical system comprising, e.g.,a focusing lens 28, a right angle prism 30, two plane mirrors 32 and 34,and a focusing lens 36. The light is incident on the MPLC laminate 10 atan angle of approximately 15° from the normal to the plane of shear.Light intensity reflected normal to the monomer-polymer interface passesthrough a focusing lens 38 and is detected with a photodetector 40connected to a digital meter 42. In this way the light due to normal,i.e., specular, reflection from the liquid crystal surface is isolatedfrom reaching the photodetector 40. By adjusting the photodetectoraperture and the slit width of the monochromator, the reflectionintensity from a sample area of ˜0.2 cm×0.5 cm is measured as a functionof the air flow differential pressure (ΔP) and the wavelength (λ) of theincident light.

Typical variations of the reflected light intensity as a function of thegas flow differential pressure at two wavelengths of 580 nm and 600 nmare shown in FIG. 5(a) and 5(b) respectively. In both cases, thereflected light intensity (I) increases as the gas flow differentialpressure (ΔP) is increased from zero. For each wavelength λ, I attains amaximum value at a certain ΔP beyond which it falls rapidly. For a givenΔP, the wavelength λ_(s) corresponding to the maximum value I_(max) inΔP versus I curve is the wavelength for the selective reflection. Forthe range of applied differential pressures used in the presentapplication, the ΔP corresponding to the peak in I decreases linearly asthe wavelength λ increases. For example, for λ=580 nm in FIG. 5(a), thepeak in I was observed at 84 mmHg whereas for λ=600 nm, it was observedat 71 mmHg. Accordingly, a series of relationships between ΔP and peakintensities for specific wavelengths are determined. These predeterminedmeasurements of the peak intensity as a function of ΔP at knownwavelengths allow a determination of the wavelength λ_(s) of theselective reflection as a function of the applied differentialpressures, as shown in FIG. 6. The variation of λ _(s) with ΔP is linearwith a slope of ˜2 nm/mmHg. Of course, the particular curves shown byexample in the Figures can be stored in a computer and comparisons madewith a test wavelength to determine pressure and shear stress on-line.

The mechanism of the selective reflection from the free surface of theliquid crystal may be understood from the geometrical representation ofthe helical structure in FIGS. 7(a)-(d). Referring to FIG. 7(a), in theGrandjean texture the helix is aligned along the z-axis, the normal tothe surface of planar orientation in the x-y plane. Light of wavelengthλ_(s) incident obliquely on the surface is selectively reflectedaccording to the relation psinθ=λ_(s) as shown in FIG. 7(b), where p isthe pitch length of the helix and θ is the angle of reflection. If aforce F is applied along the x-axis as shown in FIG. 7(c), then in thelimit when the force is small so that the helix tilts by an angle αwithout deformation, the condition for selective reflection according toFIG. 7(d) is given by pcosαsinθ=λ_(s) ', where λ_(s) ' is the newwavelength of selective light. reflection and pcosα=p' is the apparentpitch seen by the incident Under the condition of small α,λ_(s) '<λ_(s).For a well defined angle of incidence and angle of viewing the shift(λ_(s) -λ_(s) ') can be calculated as:

    λ.sub.s -λ.sub.s '=(p/2)α.sup.2 sin θ.(1)

The director equation of motion for a shear stress F applied along x canbe given by the comparison of the elastic and the viscous torques. Fromthese calculations, the tilt α is written as:

    α=(η/Kq.sub.0.sup.2 d)V.sub.x                    (2)

where d is the sample thickness, η is the coefficient of viscosity ofthe liquid crystal, K is the elastic constant related to the helix tilt,q₀ =2π/p is the helix wavevector and V_(x) is the director velocityalong x due to F. Assuming that F is large enough to force the helix totilt and the director velocity is proportional to the velocity of thegas due to the differential pressure ΔP, V_(x) from Torricelli's theoremand Bernoulli's equation governing the flow of fluid through a jet, isgiven by:

    V.sub.x =A(2ΔP/ρ)1/2                             (3)

where A is the constant of proportionality related to the skin frictionand ρ is the density of the air. Substitution of V_(x) from equation (3)in equation (2) results in:

    α=Aη(2ΔP/ρ)1/2(Kq.sub.0.sup.2 d).      (4)

From equations (1) and (4), the wavelength λ_(s) ' of selectivereflection corresponding to the air flow differential pressure ΔP can becalculated to be:

    λ.sub.s '=λ.sub.s -{2πA.sup.2 η.sup.2 /(K.sup.2 q.sub.0.sup.5 d.sup.2 ρ)}ΔP.                    (5)

Equation (5) is the equation defining the linear variation of theselective reflection wavelength as a function of the air differentialpressure (ΔP) in FIG. 5. The quantity in the { } brackets of equation(5) is the slope (˜2 nm/mmHg) of the line in FIG. 6. Thus equation (5)for λ_(s) ' in terms of ΔP can be written as:

    λ.sub.s '=λ.sub.s -βΔP            (6)

    i.e.,

    (λ.sub.s -λ.sub.s ')/β=ΔP         (7)

where the constant β is the slope of the line in FIG. 6. Equation (6) isthe equation of the linear variation of the wavelength with ΔP.

Characteristics of a liquid crystal system, comprised of a shearsensitive cholesteric monomer liquid crystal thin film coated on aliquid crystal polymer substrate, have been described. The systemprovides stable Grandjean texture, a desirable feature for shear stressmeasurements using selective reflection from the monomer liquid crystalhelix structure. Impingement of gas or air flow on the monomer liquidcrystal free surface changes the wavelength of the selective reflectionfor an incident white light from red toward blue with increase in therate of gas flow. The contrast of the selectively reflected lightimproves considerably by providing a thin, light absorbing black coatingat the monomer-polymer interface. The coating thickness is such that thesteric interactions are still sufficiently strong to maintain Grandjeantexture. For a small angle of incidence (˜15°) of a monochromatic light,the measurement of the reflected light intensity normal to themonomer-polymer liquid crystal interface enables a determination of thewavelength (λ_(s)) for selective reflection as a function of the gasflow differential pressure (ΔP) applied in the plane of the interface.In the range of the ΔP (0-100 mmHg) used in the present invention, thevariation of λ_(s) with ΔP is linear with a slope ˜2 nm/mmHg.Furthermore, the shear stress effects are reversible unlike for monomerliquid crystal--metal systems used so far for flow visualization onwind-tunnel surfaces. Thus the present invention offers a suitablemethod for direct on-line measurement of shear stress field frommeasurement λ_(s) for an incident white light.

Many modifications, substitutions, and improvements will be apparent tothe skilled artisan without departing from the spirit and scope of thepresent invention as described herein and defined in the followingclaims.

We claim:
 1. A method of determining shear stress of an article exposed to a force, the method comprising the steps of:applying a liquid crystal polymer substrate to a test surface of the article; coating an upper surface of the liquid crystal polymer substrate with a light absorbing coating; overlying the light absorbing coating with a liquid crystal monomer thin film, wherein the light absorbing coating is coated thin enough onto the liquid crystal polymer substrate to permit steric interactions between the liquid crystal polymer substrate and the liquid crystal monomer thin film to maintain the Grandjean texture to hold the thin film in place; directing light waves through the liquid crystal monomer thin film, wherein the light waves are reflected by the liquid crystal monomer thin film, wherein the coating absorbs light unreflected by the liquid crystal monomer thin film; sensing the wavelength of the reflected light waves; and correlating the sensed wavelength with the shear stress experienced by the test surface of the article.
 2. The method according to claim 1, wherein the light absorbing coating is a lacquer paint.
 3. The method according to claim 1, wherein the light absorbing coating is black.
 4. The method according to claim 1, wherein the applied liquid crystal polymer substrate is a wholly aromatic polyester.
 5. The method according to claim 1, wherein the light waves are directed at a predetermined angle of incidence with respect to an axis extending normal to interface between the substrate and thin film and the wavelengths are sensed along this normal axis.
 6. The method according to claim 1, wherein said correlating step comprises comparing the sensed reflected wavelength with known reflected wavelengths at various pressures to determine the shear stress experienced by the test surface of the article.
 7. The method according to claim 1, wherein said sensing step comprises sensing a peak intensity of the reflected light waves and correlating the sensed peak intensity with a particular wavelength, wherein the particular wavelength is the wavelength of the reflected light waves.
 8. The method according to claim 1, wherein the light is monochromatic. 